To determine the expression that represents the amount of money, \( m \), Kayla’s mom has to spend on each guest’s goody bag, we start by analyzing the costs and the budget.
- Total Budget: $150
- Cost of Food: $5 per person
- Number of Guests: 12 friends
First, we calculate the total cost of the food for 12 friends:
\[ \text{Total cost of food} = 12 \times 5 = 60 \]
Next, we subtract the food cost from the total budget to find out how much money remains for the goody bags:
\[ \text{Remaining budget for goody bags} = 150 - 60 = 90 \]
Now, let \( m \) be the amount Kayla's mom wants to spend on each goody bag. Since there are 12 friends, the total amount spent on goody bags will be \( 12m \).
Therefore, the equation representing the situation is:
\[ 12m = 90 \]
To express this in terms of the original total budget, the equation derives from the idea that the food cost ($60) plus the total goody bag cost ($12m$) must equal the total budget ($150):
\[ 12m + 60 = 150 \]
If we rearrange this, we obtain:
\[ 12m = 150 - 60 \] \[ 12m = 90 \]
To represent the remaining budget in terms of goody bags, we can express it as:
\[ 12(m + 5) = 150 \]
Here, the $5 represents the cost of each goody bag added to the amount spent on food; however, the correct representation for what is left to be spent (the $90 remaining budget divided by the number of guests) would be:
The correct answer among the options provided is:
\[ 12(m + 5) = 150 \]
This expression represents the total budget when considering the $5 spent per person on food along with the amount \( m \) for each goody bag.
6 answers